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Themed maths

Christmas maths escape room for CBSE Class 10

The elves have locked the workshop, and the presents are stuck inside. Teams solve six locks in order; each code is needed for the next. Printable clue cards, a teacher answer key and a bonus lock, all without a calculator.

Level
CBSE Class 10 (Class 9 can try most of it)
Time
41 minutes, plus a 10-minute extension
Topics
Real numbers and arithmetic progressions; Polynomials: zeroes; Probability and coordinate geometry
Equipment
No calculator. Every answer is a whole number.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: lock 16 minThe wrapping room
Main: lock 26 minThe list
Main: lock 36 minThe star
Main: lock 46 minThe polynomial lock
Main: lock 56 minThe dice
Main: lock 66 minThe workshop door
Extension10 minFast finishers or homework

Starter (5 minutes)

Warm-up before the locks: quick questions on the board.

  1. Find the LCM of 4 and 6.
  2. Work out 32 + 42.
  3. Find the next term of the AP 7, 11, 15, …

Main activity (36 minutes)

Lock 1: The wrapping room (6 min)

Ribbons of 84 cm and 120 cm are cut into equal pieces, as long as possible, with nothing left over.

  1. Find the length of each piece: the HCF of 84 and 120. This is code 1.

Lock 2: The list (6 min)

The elves number their list with an AP.

  1. Find the term of the AP 5, 9, 13, … whose position is code 1. This is code 2.

Lock 3: The star (6 min)

A star is hung from the top of the tree.

  1. Work out √(code 2) × 11. This is code 3.

Lock 4: The polynomial lock (6 min)

The lock shows p(x) = x2 − kx + 12, where k = code 3 − 70.

  1. Find the zeroes of p(x). Their product is code 4.

Lock 5: The dice (6 min)

A fair die is thrown once.

  1. Find the probability of a number less than 5, then multiply it by code 4. This is code 5.

Lock 6: The workshop door (6 min)

The last lock.

  1. Find the distance between (0, 0) and (code 5 − 2, 8). It opens the door.

Extension (10 minutes)

Bonus lock for the fastest team.

  1. A conical party hat has radius 7 cm and height 24 cm. Find its slant height and its curved surface area. (Use π = 22/7.)

For teachers

Teacher notes and full worked answers
  • How to run it: print the student sheet and cut out the six lock cards. Give each team lock 1. When a team brings you the right code, give them the next card (the answer key is in the answers PDF). The first team to open lock 6 escapes. Teams can also have every card at once and race through them in order.
  • Each code is used in the next lock, so check every code before the team moves on: one slip early on breaks the chain.

Starter

  1. 12
    • Multiples of 6: 6, 12; 12 is also a multiple of 4.
  2. 25
    • 9 + 16 = 25
  3. 19
    • d = 4

Lock 1: The wrapping room

  1. 12
    • 84 = 22 × 3 × 7, 120 = 23 × 3 × 5
    • HCF = 22 × 3 = 12

Lock 2: The list

  1. 49
    • an = 5 + (n − 1) × 4
    • a12 = 5 + 44 = 49

Lock 3: The star

  1. 77
    • √49 = 7
    • 7 × 11 = 77

Lock 4: The polynomial lock

  1. 3 and 4; code 12
    • k = 7: x2 − 7x + 12 = (x − 3)(x − 4)
    • 3 × 4 = 12 (the product of the zeroes is c/a = 12)

Lock 5: The dice

  1. 8
    • P = 4/6 = 2/3
    • 2/3 × 12 = 8

Lock 6: The workshop door

  1. 10
    • The point is (6, 8).
    • √(36 + 64) = 10

Extension

  1. Slant height 25 cm; curved surface area 550 cm2
    • l = √(49 + 576) = 25
    • πrl = 22/7 × 7 × 25 = 550

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

Practise the topics

Numbers round and word scramble maths · End-of-year quiz maths · Spot the mistake relay and maths taboo maths · All themed maths

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